Derivative Of Field Research Articles

Current recovery for the RWG‐based method of moments

Derivative recovery through local smoothing, is a well-known approach to obtain an estimate of a solution field's derivative, to one polynomial order higher than its direct representation. In the finite element method context, this is often referred to as ‘gradient recovery’. The method of moments (MoM) is routinely used to solve electromagnetic field integral equations in terms of the electric surface current density, which is often represented by mixed first-order, Rao–Wilton–Glisson (RWG) basis functions upon a mesh of triangle elements. A procedure for recovering a mixed second-order, approximate solution from an RWG-based MoM solution is presented. Recovery of the solution itself rather than its derivative, is made possible by exploiting specific properties of the mixed-order, surface divergence-conforming function spaces. The procedure is not strictly local, however, only sparse, positive-definite global linear systems must be solved. The procedure is independent of the integral operator. Computational complexity is lower than that of existing residual-based MoM error estimators. Results are shown with the recovered solution being a better approximation than the original solution. The procedure is useful for post-processing and for local or global a posteriori error estimation. It can be incorporated into any RWG-based MoM code.

Dromion Interactions of (2+1)-Dimensional KdV-type Equations

Starting from a two line soliton solution of an integrable (2+1)-dimensional equation in bilinear form, one can find a dromion solution, that is localized in all directions, for the physical field and/or the suitable potential (the physical field's derivatives). The interaction properties between two dromions are studied both analytically and numerically for (2+1)-dimensional KdV-type equations. Our analysis shows that the shape of dromions after interaction may be changed or unchanged for different form of solutions.

Interaction of Solitons in (2+1)-Dimensional Integrable Models

Starting from a two line soliton solution of an integrable (2+1)-dimensional system in bilinear form, one can find a dromion solution that is localized in all directions for the physical field and/or the suitable potential (the physical field's derivatives). The interaction between two dromions is studied both analytical and numerical for the (2+1)-dimensional Nizhnik-Novikov-Veselev equation and the modified Korteweg-de Vries (mKdV) equation. The interaction may be elastic (without shape and velocity deformation) or inelastic depending on the form of multisoliton solution.

Novel boundary condition for the finite-element solution of arbitrary planar junctions

A novel boundary condition for a two-dimensional finite-element method (2D-FEM) is developed to simulate accessing waveguides to planar optical junctions. This new boundary condition is based on a paraxial approximation to the field's derivatives over the junction's ports. The formulation is very easily adapted within the 2D-FEM framework while providing good simulation results. Two examples are provided to show the applicability and reliability of the present method: a waveguide step discontinuity and a sharp waveguide bend.